Mathematical Physics and Harmonic Analysis Seminar

Date: April 4, 2025

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Markus Pflaum, University of Colorado

Title: Representations of energy landscapes by sublevel set persistent homology

Abstract: Given a molecular Hamiltonian, its first potential energy eigenfunction in the Born-Oppenheimer approximation, the electron density and the electron localization functions are functions from chemistry which provide crucial information about the conformations, dynamics and reactibility of the molecule. In the DELTA project (Descriptors of Energy Landscapes by Topological Analysis) the surfaces spanned by these functions are examined by methods stemming from topology and singularity theory. The talk will give an overview of methods applied and results achieved by the DELTA group. In the case of n-alkanes, the sublevel persistent homology of the energy landscape and a visual representation of its Morse-Smale complex for n small could be determined. Using methods from real algebraic geometry and statistics we also present in this talk a method for learning the underlying variety of a data set which in our scenario comes from a molecular potential energy surface or one of its reductions. We explain numerical methods how to find singularities and conclude the talk with an application to the conformational space of cyclooctane. The talk is on joint work with H. Adams, A. Clark, Y. Zhang, E. AlSai, H. Jordan, P. Gara, J. Mirth et al.